lim x→0(1-cosxcos2x...cosnx)/(x^2)
=lim(sinx/cosx+2sin2x/cos2x+...+nsinnx/cosnx)cosxcos2x...cosnx/(2x)
=1/2lim(tanx/x+2tan2x/x+...+ntannx/x)cosxcos2x..cosnx
=1/2(1+2^2+3^2+...+n^2)*1
=n(n+1)(2n+1)/12
求极限(1-cosxcos2x...cosnx)/(x^2) (lim x->0)
lim x→0(1-cosxcos2x...cosnx)/(x^2)
=lim(sinx/cosx+2sin2x/cos2x+...+nsinnx/cosnx)cosxcos2x...cosnx/(2x)
=1/2lim(tanx/x+2tan2x/x+...+ntannx/x)cosxcos2x..cosnx
=1/2(1+2^2+3^2+...+n^2)*1
=n(n+1)(2n+1)/12